It was a sight no one could have anticipated. The Lehman Brothers employees carrying boxes of belongings out of the bank's London HQ seemed like well-heeled refugees fleeing a financial war zone, trying to comprehend the events that had turned their world upside down. Lehman's size and, more important, trading connections with other firms had made it one of the select group assumed to be "too big to fail". But, almost two years ago, it did.

No firm should be considered too big to fail, but the interwoven nature of the financial system, which provides some of its resilience, also brings one of its weaknesses. The failure of a firm that is systemically important can set off a line of falling dominoes around the system – a threat that led the UK and US governments to invest billions to shore up the system, taking stakes in such institutions as Royal Bank of Scotland.

While few would still argue that the banks should not have been supported, it is clear that taxpayers should never again be the first to be called upon in a banking crisis. The assumption that some financial institutions are so essential that they will always be rescued removes a necessary business discipline and absolves management of its responsibilities. It also distorts competition: after all, where would you put your money – in the bank that is implicitly guaranteed, or the one that isn't?

Banks, like any businesses, must be allowed to fail. But when that failure threatens other institutions and the wider economy we need a way to head off the threat of contagion just before the point of collapse.

One idea is a rapid recapitalisation under which the bank's creditors would convert their claims into ownership. There are two likely ways of doing this. Under the first, called "bail-in", some of the bank's unsecured debt would automatically convert into equity if the firm hit an agreed trigger, set by its lead regulator. There would be no requirement for the regulators to consult with shareholders or creditors, so a rescue could be mounted very quickly – over a weekend, for instance.

The other option is "contingent capital". This is an investment product, typically a bond, that converts into shares as soon as the firm hits a predefined point – before it is teetering on the brink of insolvency and well before it becomes legally insolvent. Unlike bail-in, there is no need for regulators to become involved and, as the terms of the conversion are agreed at the time the investment is made, it is a completely transparent process so the market can see what is happening and be reassured.

Either option would be preferable to liquidation. Both protect depositors and reduce the impact on employees, since recapitalisation would enable the firm to continue in business, significantly reducing the likelihood of contagion. Having such mechanisms in place would help to maintain confidence in a bank's ability to meet its commitments, which in turn would maintain confidence in other banks exposed to the failing firm. Crucially, there is no requirement for capital support by taxpayers or a pre-capitalised fund for providing liquidity.

In the case of Lehman, we estimate a bail-in would have recovered 85% to 95% of what the senior unsecured creditors were owed, and the firm might well have avoided liquidation altogether.

Who loses? Principally, the shareholders would bear the loss through dilution or even complete elimination of their equity. That is all part and parcel of being a shareholder. And while the existing management may have a part to play in ensuring that the regulators and advisers have the necessary information to assist them, it is not hard to envisage that a failure of this nature would lead to a change of leadership.

These new ideas are starting to attract interest. The G20 has asked its financial stability board to report on both options at the Seoul summit in November, and there has been interest from regulators in the UK, US and Europe. There are still legal and technical issues that would have to be addressed, not least of which would be dealing with firms operating in multiple jurisdictions. However, schemes using bail-in or contingent capital could not only render obsolete the notion of taxpayers bailing out firms that are too big to fail, but also expose the forcible breaking-up of universal banks as a completely pointless exercise.